"What an extraordinary election, quite extraordinary," said Adnan Pachachi, the elder statesman of Iraq and a man not easily impressed after seeing his country convulsed by war and dictatorship for half a century.

It is a strange affair. Not since the war which overthrew Saddam Hussein had there been such a gap between the reality of politics in Iraq and the picture presented by the US and British governments. The poll yesterday was portrayed as if Washington and London had finally been able to reach their goal of delivering democracy to Iraqis. In fact the US postponed elections to a distant future after the invasion of 2003.

The overthrow of Saddam Hussein had been so swift that the American administration thought it could rule Iraq directly with little Iraqi involvement. But in the autumn of 2003 the US made two unpleasant discoveries: The guerrilla attacks in Sunni districts of Iraq were increasing by the day. They were supposedly confined to "the Sunni triangle", a description with a comfortingly limited ring to it, but in reality an area larger than Britain.

The second development which Paul Bremer, the head of the US-run Coalition Provisional Authority, was slow to understand, was that an elderly Shia cleric living in an alleyway home in the holy city of Najaf had more influence than any of the former Iraqi exiles on the US payroll. In June 2003, Grand Ayatollah Ali al-Sistani, the most influential Shiah leader, issued a fatwa or religious ruling saying that those who drew up Iraq’s constitution must be elected, not nominated by the US and the Iraqi Governing Council whose members Washington had appointed. In November 2003, he issued a further ruling saying that the transitional government must be elected.

Shia leaders believed they had made a grave mistake after Britain defeated the Turkish army and occupied what became Iraq in the First World War. The Shia revolted against the British occupation in 1920 so Britain turned to the Sunni community to rule Iraq and the Sunni kept their grip on power under the monarchy, the Republic and the dictator.

The reason there was a poll yesterday was that the US, facing an increasingly intensive war against the five million Sunni, dared not provoke revolt by the 15 to 16 million Shia. The price the US paid was to have an election in which the Shia would show that they are a majority of Iraqis.

But will the election yesterday involve a real transfer of power to the Shia? Last June, Iraqi sovereignty was supposedly transferred to the US-appointed interim government of Iyad Allawi. The change was largely a mirage. The government still depends for its existence on the presence of 150,000 US troops.

The wall-to-wall media coverage of the election yesterday obscured several of the realities of political life in Iraq. The National Assembly now being elected will have limited powers. It is constituted so no single community can dominate the others. But, as in Lebanon, this may be a recipe for paralysis. The assembly must elect a president and two vice-presidents and they will in turn chose a prime minister and ministers. The successful candidate will be the person with the fewest enemies.

The Shia were not going to the polling stations for the pleasure of risking mortars and suicide bombers. Their leaders have told them they will obtain real power for the first time.

Some US commentators have wondered if Washington might not be able to hold Iraq or at least remain in covert control by relying on the Kurds and the Shia. Together they make up 80 per cent of the population. This is known as ‘the 20 per cent solution" whereby the US will be able to deal with a rebellion supported by the Sunni Arabs, 20 per cent of the population.

This policy is based on a misconception. The Sunni are resisting the US occupation in arms. The Shia have not joined this rebellion, though Muqtada Sadr and his Mehdi Army fought the US Marines for Najaf last August. A central feature of Iraqi politics is that since the overthrow of Saddam Hussein, the US has become steadily more unpopular in Iraq outside Kurdistan. This is true among the Shia as well as the Sunni. An opinion poll by Zogby International shows that the Sunni Arabs who want the US out now or very soon total 82 per cent. The proportion of Shia wanting the US to go is less than the Sunni but still overwhelming at 69 per cent. Shia religious leaders have been telling their followers to vote as the quickest way to end the occupation.

The enthusiasm with which so many Shia went to the polls is a double-edged weapon. They did so in the belief that their ballots would translate into power.

In the immediate future, the election changes little in Iraq. The world is full of parliaments duly elected by a free ballot but power stays elsewhere, with the army, the security services or, in the case of Iraq today, an occupying foreign power.